Q. 255.0( 1 Vote )

An urn contains 3 white and 6 red balls. Four balls are drawn one by one with replacement from the urn. Find the probability distribution of the number of red balls drawn. Also, find mean and variance of the distribution.

Answer :

Given: An urn contains 3 white and 6 red balls


To find: the probability distribution of the number of red balls drawn and mean and variance of the distribution


Let X denote the number of red balls drawn in four balls from total of 9 balls


X can have five value, i.e. 0, 1, 2, 3, 4 as there are 6 red balls


Now,


Probability of getting 0 red ball = P(X=0)








The probability of getting 1 red ball = P(X=1)








The probability of getting 2 red balls = P(X=2)







The probability of getting 3 red balls = P(X=3)







The probability of getting 4 red balls = P(X=4)








Probability Distribution Table





Formula used:




Therefore,





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